Answers
Answer:
Hey there!
Triangle PQT and RQT are congruent by AAS. AAS means that one side is congruent, and two angles are congruent.
Since these triangles share one side, then the side is congruent.
PR is a straight line, so if angle Q is 90 degrees, then the supplementary angle is also 90 degrees.
Finally, the diagram shows that angles R and P are congruent to each other.
Hope this helps :)
Related Questions
The real numbers $x$ and $y$ are such that \begin{align*} x + y &= 4, \\ x^2 + y^2 &= 22, \\ x^4 &= y^4 - 176 \sqrt{7}. \end{align*}Compute $x - y.$
Answers
You get everything you need from factoring the last expression:
[tex]x^4-y^4=-176\sqrt7[/tex]
The left side is a difference of squares, and we get another difference of squares upon factoring. We end up with
[tex]x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)[/tex]
Plug in everything you know and solve for [tex]x-y[/tex]:
[tex]-176\sqrt7=(x-y)\cdot4\cdot22\implies x-y=\boxed{-2\sqrt7}[/tex]
Answer:
-2sqrt(7)
Step-by-step explanation:
Solution:
From the third equation, $x^4 - y^4 = -176 \sqrt{7}.$
By difference of squares, we can write
\[x^4 - y^4 = (x^2 + y^2)(x^2 - y^2) = (x^2 + y^2)(x + y)(x - y).\]Then $-176 \sqrt{7} = (22)(4)(x - y),$ so $x - y = \boxed{-2 \sqrt{7}}.$
What is the length of leg y of the right triangle?
84
85
O1
09
O 13
O 26
Answers
Answer:
[tex] \boxed{\sf Length \ of \ leg \ y = 13} [/tex]
Step-by-step explanation:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
[tex] \therefore \\ \sf \implies {84}^{2} + {y}^{2} = {85}^{2} \\ \\ \sf {84}^{2} = 7056 : \\ \sf \implies 7056 + {y}^{2} = {85}^{2} \\ \\ \sf {85}^{2} = 7225 : \\ \sf \implies 7056 + {y}^{2} = 7225 \\ \\ \sf Substract \: 7056 \: from \: both \: sides : \\ \sf \implies (7056 - 7056) + {y}^{2} = 7225 - 7056 \\ \\ \sf 7056 - 7056 = 0 : \\ \sf \implies {y}^{2} = 7225 - 7056 \\ \\ \sf 7225 - 7056 = 169 : \\ \sf \implies {y}^{2} = 169 \\ \\ \sf 169 = {13}^{2} : \\ \sf \implies {y}^{2} = {13}^{2} \\ \\ \sf \implies y = \sqrt{ {13}^{2} } \\ \\ \sf \implies y = {13}^{ \cancel{2} \times \frac{1}{ \cancel{2}} } \\ \\ \sf \implies y = 13 [/tex]
So,
Length of leg y of the right triangle = 13
EXPLANATION:
(Using Pythagoras Theorem)
c^2 - a^2 = b^2
85^2 - 84^2 = b^2
7225 - 7056 = b^2
169 = b^2
√169 = b
b= 13
I HOPE THIS HELPED:)
2/3 of 27 equal 25% of a number
Answers
Answer:
The number is 72
Step-by-step explanation:
2/3*27 = 2*9 = 18
so 18 = 25%
25% = 1/4
so 1/4 = 18/?
so ? = 18*4 = 72
Answer:
x=72
Step-by-step explanation:
This is an easy equation.
2/3*27=25/100x
solve.
2/3 * 27 is 18
18=25/100x
Divide. (25/100 can be converted to 1/4
Divide 18 by 1/4x
x=72!
Cheers, I hope you can understand.
My age if I am half as old as two more than twice Mack's age if Mack is m years old.
Answers
Answer:
You are m + 1 years old.
Step-by-step explanation:
Let's say that you are x years old, and Mack is m years old.
x = 1/2( two plus twice m)
x = 1/2(2 + 2m)
x = 1 + m
x = m + 1
Hope this helps!
find the solution of x and y
Answers
Answer:
x = 1.25, y = 1.75
Step-by-step explanation:
The smaller and larger triangles are similar triangles. (the 2 triangles have the same angles).
We know that the smaller triangle has length 8 for it's bottom side when the larger triangle has length 10. This means the scale factor between the 2 is 10 / 8 which is 1.25. Therefore by multiplying the side lengths of the smaller triangle by 1.25 we get the side lengths of the larger triangle.
5 * 1.25 = 6.25
7 * 1.25 = 8.75
However we don't want the whole side lengths we want x and y, We need to subtract 5 and 7 respectively from the lengths of the larger triangles.
Therefore the lengths must be: 6.25 - 5 = 1.25
and 8.75 - 7 = 1.75
Therefore x and y equal 1.25 and 1.75
10. In a class A of 25 students, 20 passed with 60% or more marks; in another class B of 30 students, 24 passed with 60% or more marks. In which class was a greater fraction of students getting with 60% or more marks?
Answers
Answer:
class b
Step-by-step explanation:
Explaintion
This recipe makes 6 portions of fajitas. Carly has 900 g of chicken, 1200 g of peppers, 150 g of onion, 60 g of spice mix and 30 tortillas. How much more of each ingredient will she need to make 18 portions by following this recipe? Recipe: Serves 6 500 g chicken 600 g peppers 90 g onion 25 g spice mix 12 tortillas
Answers
Answer:
600 g chicken
600 g peppers
120 g onion
15 g spice mix
6 tortillas
Step-by-step explanation:
To make 18 portions, Carly needs to make 3 times the original recipe.
1. Solve for how much of each ingredient is needed.
500 · 3 = 1500 g chicken
600 · 3 = 1800 g peppers
90 · 3 = 270 g onion
25 · 3 = 75 g spice mix
12 · 3 = 36 tortillas
2. Subtract how much of each ingredient Carly already has from how much is needed to find how much more she needs.
1500 - 900 = 600 g chicken
1800 - 1200 = 600 g peppers
270 - 150 = 120 g onion
75 - 60 = 15 g spice mix
36 - 30 = 6 tortillas
Answer:
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Step-by-step explanation:ejbfkwej
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Because 10 is a multiple of 90
Answers
Answer: 10 is a multiple of 90
Step-by-step explanation:
90/10 = 9. Because 9 is a whole number, 10 is a factor of 90, and 90 is a multiple of 10.
Hope it helps <3
Answer:
Step-by-step explanation
:
Why is 10 a multiple of 90?
simply
10 · 9 = 90
Find the volume in cubic meters, of the 3-Dimensional composite
figure.
8m
5m
Answers
Answer:
890 m^3 to the nearest whole number.
Step-by-step explanation:
Volume = volume of the cylinder + volume of the hemisphere:
= π r^2 h + 1/2 * 4/3 π r^3
= π*5^2 * 8 + 1/2 * 4/3 π 5^3
= 890.12
The shortest side of a triangle is 12cm and the area of the triangle is 8 square cm. A similar triangle has an area of 18 square cm. Calculate the shortest side of this triangle
Answers
Answer:
27cm
Step-by-step explanation:
Given the following :
Triangle A:
Shortest side = 12cm
Area of triangle = 8cm^2
Triangle B:
shortest side =?
AREA of triangle = 18cm^2
If triangle A and B are similar :.
Area A / Area B = Length A / length B
8cm^2 / 18 = 12 / length B
Cross multiply :
8cm * Length B = 18 × 12
Length B = 216 / 8
Length B = 27
Therefore, the shortest of the other triangle IS 27cm
Answer:
its A C and E hope this helps
Step-by-step explanation:
Jackson is running a 10-mile race. He runs 1 mile every 8 minutes. Jackson's distance from this finish line after x minutes is represented by the function x+8y=80
Answers
Answer:
Jackson's distance from the finish line after x minutes will be given as;
since from the statements we know that x represents the number of minutes he had run, for us to be able to calculate his distance from the finish line we simply solve the problem mathematically as follows;
x=80-8y
Step-by-step explanation:
from the initial representation we have x+8y=80,
from the preliminary statement we know x to be the number of minutes from the start of the race to the current point Jackson.
so we assume that y in the equation represents the number of distance covered by the x minutes in miles.
that is how we end up with ;
x=80-8y.
origin is the corner of square whose one side is 3 X + 4 Y + 5 = 0 find its area.
options:
a.1
b.2
c.3
d.4
Answers
Answer:
The correct option is;
a. 1
Step-by-step explanation:
Given that the origin (0, 0) is the corner of the square
The equation of one of the sides = 3·X + 4·Y + 5 = 0
Therefore, we have;
Y = -3/4·X - 5/4
Which gives the slope as -3/4 and the y-intercept as (0, -5/4)
The sloe of the perpendicular side from the origin to the given line is therefore = -(1/(3/4)) = 4/3
The y-intercept of the current particular perpendicular side = 0
The equation is therefore;
y = 4/3·x + 0
The coordinate of the point of intersection of the two sides of the square above is found by equating the two lines to each other as follows;
4/3·x = -3/4·X - 5/4
4/3·x + 3/4·X = -5/4
25/12·X = -5/4
X = -5/4×12/25 = -3/5
Y = 4/3·x = 4/3× (-3/5) =-4/5
The length of a side = √((-3, 5) - 0)² + ((-4, 5) - 0)² = √1 = 1
The area of a square = (Length of side) × (Length of side)
∴ The area of the square = 1 × 1 = 1
The area of the square = 1.
URGENT! Please help me with this question.
Answers
Step by step is below
Hopefully this help you
:)
Bao can eat 12 chicken wings in 3 minutes.She eats the chicken wings at a constant rate how many chicken wings can bao eat in 12 minutes
Answers
Answer:
48 wings
Step-by-step explanation:
12:3 is the ratio. So multiply both of it by 4. Then it would be 48:12
Answer:
48 chicken wings
Step-by-step explanation:
If Bao can eat 12 chicken wings in 3 minutes and 12 minutes is 3 minutes times 4, then the answer would be 12 chicken wings times 4, so 12 times 4, which is 48, so the answer would be 48 chicken wings.
What is the volume of a cone when the radius is 6 and the height is 13
Answers
Answer:
489.84 units³Step-by-step explanation:
Given,
Radius ( r ) = 6
Height ( h ) = 13
Volume of cone = ?
Now, Let's find the volume of cone:
[tex] = \pi \: {r}^{2} \frac{h}{3} [/tex]
plug the values
[tex] = 3.14 \times {6}^{2} \times \frac{13}{3} [/tex]
Evaluate the power
[tex] = 3.14 \times 36 \times \frac{13}{3} [/tex]
Calculate
[tex]489.84[/tex] units³
Hope this helps..
Best regards!!
Mr. SMITH had 4 daughters, each daughter had a brother ... How many sons does Mr. Smith have?
Answers
He tells us that the 4 daughters have a brother, so, since they belong to the same family, the sisters are the same because they have only one brother.
Answering our question:
or Mr. Smith has 4 daughters and also 1 son.
Answer:
one son
Step-by-step explanation:
each daughter had a brother, means there is only one son
Mr. smith has 1 son
Directions: For
1.what is the square root
361
Answers
Answer:
√361=19
Step-by-step explanation:
Solve and CHECK the following:
8−(5x−2)=6−2(3x+1)
Answers
Answer:
X=6/11
Step-by-step explanation:
8-(5x-2)=6-2(3x+1)
8-5x+2=6-6x-2
10-5x=4-6x
6=11x
x=6/11
Answer:
8-5x-2=6-6x+2
8-2-6-2=5x-6x
-10+8=-x
-2 =-x
x=2 ........×-1
x=2
The electromotive force V of an alternating current circuit at time t can be describe by the
following function, where V is volts and t is in seconds. V(t) = 220sin(180πt). How many cycles
will the circuit run through in 1 minute?
Answers
Answer:
5400 cycles
Step-by-step explanation:
You have the following function:
[tex]V(t)=220sin(180\pi t)[/tex]
where t is in seconds.
In order to find the number of cycles in 1 minute, you first calculate the frequency of the function, which is given by:
[tex]f=\frac{180\pi}{2\pi}=90s^{-1}[/tex]
The number of cycles is then given by:
[tex]n=ft=(90s^{-1})(60s)=5400\ cycles[/tex]
There are 5400 cycles in 1 minute
It’s timed please help
Answers
Answer:
4 is included in the domain
Step-by-step explanation:
50. At a booth at the school carnival in past years, they've found that 32% of students win a stuffed toy ($3.25), 10% of students win a jumprope ($1.70), and 8% of students win a t-shirt ($7.80). The remaining students do not win a prize. If 200 students play the game at the booth, how much money should the carnival committee expect to pay for prizes for that booth
Answers
Answer:
The expected amount to be paid by the carnival committee for prices would be $366.80
Step-by-step explanation:
Hello!
Here, we want to calculate the amount of money the carnival committee is expected to pay for the prizes for that booth
From the question, we have 3 categories of prices to be won
To calculate for people that won’t win anything , we simply subtract the percentages of all from 100
That would be 100-32-10-8 = 100-50 = 50%
So now let’s calculate the number of people out of 200 that will win each category based on the percentages
For stuffed toy
32/100 * 200 = 64
Jump rope
10/100 * 200 = 20
For t-shirt
8/100 * 200 = 16
So total price paid for stuffed toy= 3.25 * 64 = $208
For jump rope, we have 1.7 * 20 = $34
For t-shirt , we hav 16 * 7.8 = $124.8
So the total value spent on prices by the committee would be;
124.8 + 34 + 208 = $366.80
A new parking lot is being built for a medical office. The expression representing the number of parking spots in the new lot is 15 x over 4 minus 9, where x represents the number of parking spots in the first row. How many spots are in the parking lot if there are 32 parking spots in the first row? 79 88 111 129
Answers
Answer: 111
Step-by-step explanation:
[tex]\frac{15}{4} x - 9[/tex] is the expression and we know that x is the number of parking spots in the first row. The plot in 32 for x and solve.
[tex]\frac{15}{2} (32) - 9[/tex]
120 - 9 = 111
Answer:
sorry for the late answer
Step-by-step explanation: its c : 111
Find the slope and y-intercept of the following graph.
Answers
Answer: y = -5*x + b
Step-by-step explanation:
A line is written as:
y = a*x + b
where a is the slope and b is the y-intercept.
IIf we have a line that passes through the points (x1, y1) and (x2, y2) then the slope of the line is:
a = (y2 - y1)/(x2 - x1)
In this case we can see that the line passes through the points:
(0, 2) and (1, - 3)
Then the slope is:
a = (-3 - 2)/(1 - 0) = -5
Then our line is:
y = -5*x + b
And when x = 0, y = 2 then:
y = 2 = -5*0 + b
2 = b
Our line is:
y = -5*x + b
Use the linear combination method to solve this system of equations. What is the value of x? Negative 2.4 x minus 3.6 y = 1.2. 2.4 x + 1.2 y = 1.2. Negative 1 0 1 -4.8
Answers
Answer:
x=1/4
y=1/2
Step-by-step explanation:
Given:
-2.4x+3.6y=1.2
2.4x + 1.2y=1.2
-2.4x+3.6y=1.2
Divide through by 1.2
-2x+3y=1
2.4x + 1.2y=1.2
Divide through by 1.2
2x+y=1
-2x+3y=1 (1)
2x+y=1 (2)
From 2
y=1-2x
Substitute y=1-2x into (1)
-2x+3y=1
-2x+3(1-2x)=1
-2x+3-6x=1
-8x=1-3
-8x=-2
Divide both sides by -8
x=1/4
Substitute x=1/4 into (2)
2x+y=1
2(1/4)+y=1
2/4+y=1
1/2+y=1
y=1-1/2
y=1/2
x=1/4
y=1/2
Answer:
x=1
Step-by-step explanation:
edge 2021
THE LANDSCAPER IS PLANTING A TREE THAT IS NOW 55 CM TALL. THE TREE WILL GROW 4 CM PER MONTH FOR X MONTHS. THE TREE WILL GROW TO BE AT MOST Y CM TALL. WRITE AN INEQUALITY SHOWING THIS RELATIONSHIP.
Answers
Answer: 55cm + X*4cm < Y.
Step-by-step explanation:
The initial height of the tree is 55cm
The tree will grow 4cm per month, for X months.
then the height of the tree is the initial height, plus X times 4cm
H = 55cm + X*4cm
If Y is the maximum height that this tree can grow, then we can write the inequality as:
H < Y.
55cm + X*4cm < Y.
Banita has a piece of string that is One-tenth times 7 inches long. Which fraction is equal to the length of Banita’s string?
Answers
Answer: The length is 7/10 inches.
Step-by-step explanation:
So if is says that the string is 1/10 times 7 inches long, then it represents the length of the string.
So L = [tex]\frac{1}{10}*7[/tex]
L = 7/10
Answer:
l=7/10
Step-by-step explanation:
A restaurant catered a party for 40 people. A child’s dinner (c) cost $11 and an adult’s dinner (a) cost $20. The total cost of the dinner was $728. How many children and adults were at the party? Use the table to guess and check. 8 children and 32 adults 9 children and 31 adults 10 children and 30 adults 12 children and 28 adults
Answers
Answer:
x=8 number of children
y=32 number of adults
Step-by-step explanation:
x be children and y for adults
x+y=40 ⇒ y=40-x
11x+20y=728 solve by substitution of y=40-x
11x+20(40-x)=728
11x+800-20x=728
-9x=728-800
x=72/9 ⇒ x=8 number of children
y=40-x
y=40-8⇒ y=32 number of adults
While standing in front of the school
Answers
Answer:
Step-by-step explanation:
what do u see!????????
Which two of the following numbers round to 752.3 if we're rounding to the nearest tenth? Choose 2 answers: a 752.32 b 752.27 c 752.36
Answers
A, B is the answer..................
Answer:
its A and C
Step-by-step explanation:
Just because...........
The value of 3x+2 is 9 plus twice the value of x+5. What is x?
Answers
Answer:
17
Step-by-step explanation:
3x+2 = 9 + 2(x+5)
3x + 2 = 9 + 2x + 10
3x + 2 = 2x + 19
x = 17
Answer:
[tex]\huge\boxed{x=17}[/tex]
Step-by-step explanation:
[tex]3x+2=9+2(x+5)\qquad\text{use the distributive property}\\3x+2=9+(2)(x)+(2)(5)\\3x+2=9+2x+10\\3x+2=2x+19\qquad\text{subtract 2 from both sides}\\3x+2-2=2x+19-2\\3x=2x+17\qquad\text{subtract}\ 2x\ \text{from both sides}\\3x-2x=2x-2x+17\\x=17[/tex]